The Teumessian fox was a gigantic fox that was destined never to be caught.
The fox was one of the children of Echidna. It was said that it had been sent by the gods (perhaps Dionysus) to prey upon the children of Thebes as a punishment for a national crime. Creon, the then Regent of Thebes, set Amphitryon the impossible task of destroying this beast.
He discovered an apparently perfect solution to the problem by fetching the magical dog Laelaps, who was destined to catch everything it chased, to catch the Teumessian fox. Zeus, faced with an inevitable contradiction due to the paradoxical nature of their mutually excluding abilities, turned the two beasts into stone. The pair were cast into the stars, and remain as Canis Major (Laelaps) and Canis Minor (Teumessian Fox).